Quantum automorphism groups of vertex-transitive graphs of order $\leq 11$

On the quantum symmetry of distance-transitive graphs

In this article, we study quantum automorphism groups of distance-transitive graphs. We show that the odd graphs, the Hamming graphs $H(n,3)$, the Johnson graphs $J(n,2)$ and the Kneser graphs $K(n,2)$ do not have quantum symmetry. We also give a table with the quantum automorphism groups of all cubic distance-transitive graphs. Furthermore, with one graph missing, we can now decide whether or not a distance-regular graph of order $\leq 20$ has quantum symmetry. Moreover, we prove that the Hoffman-Singleton graph has no quantum symmetry. On a final note, we present an example of a pair of grap…

$3$-传递图的量子对称性

Quantum symmetry of $3$-transitive graphs

本文利用平面代数计算了大部分1985年分类的3-传递图的量子自同构群，证明部分图无量子对称性，部分仿射极图的量子自同构群与经典群幺半等价。

12顶点上顶点传递图的量子对称性

Quantum Symmetries of Vertex-Transitive Graphs on 12 Vertices

本文扩展了图的量子自同构群研究，确定了所有12顶点顶点传递图的量子对称性，并明确给出了大多数图的量子自同构群，填补了该领域顶点数研究的空白。

Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces

We study quantum automorphism group of vertex-transitive graphs using intertwinner spaces of the magic unitary matrix associated to this quantum subgroups of $S_n^+$. We also give some applications to quantum symmetries of circulant graphs as $C_{13}(3,4)$ and $C_{17}(2,4,8)$.

Improved bound on the non zero eigenvalues of the graph Laplacian coming from quantum symmetry of vertex transitive graphs

A chain of quantum subgroups of the quantum automorphism group of finite graphs has been introduced. It generalizes the construction of J. Bichon (see [3]) in a sense. A better bound of the non zero eigenvalues of the graph Laplacian has been obtained using the chain of quantum subgroups.